from manim import *
class CustomCurve(VMobject):
    def __init__(self, **kwargs):
        super().__init__(**kwargs)
        # 定义自定义曲线的控制点
        points = [
            [15, 20, 0],
            [14,15,0],
            [10, 12.5, 0],
            [14,10,0],
            [15, 5, 0],
            
        ]
        self.set_points_smoothly(points)

class CustomCurve1(VMobject):
    def __init__(self, **kwargs):
        super().__init__(**kwargs)
        # 定义自定义曲线的控制点
        points = [
            [25, -15, 0],
            [20,-20,0],
            [25,-25,0],
        ]
        self.set_points_smoothly(points)



class math1(MovingCameraScene):
    def construct(self):
        self.camera.background_color = BLACK  # 设置背景颜色
        self.camera.frame_width = 100  # 设置边框宽度
        self.camera.frame_height = 60  # 设置边框高度
        self.camera.pixel_height = 1080  # 设置像素高度
        self.camera.pixel_width = 1920  # 设置像素宽度
        self.camera.center = ORIGIN  # 设置中心点位置
        self.camera.scale_factor = 1.0  # 设置缩放因子

        #设置横线
        for i in range(6*2+1):       
            dot1=Dot([-50,5*(i-6),0]).set_opacity(0.5)
            dot2=Dot([50,5*(i-6),0]).set_opacity(0.5)
            if i==6:
                line1=Line(dot1,dot2).set_color(WHITE).set_opacity(0.5)
                
            else:
                line1=Line(dot1,dot2).set_color(WHITE).set_opacity(0.5)
               
            self.add(dot1,dot2,line1)
        #设置竖线
        for i in range(10*2+1):        
            dot3=Dot([(i-10)*5,-30,0]).set_opacity(0.5)
            dot4=Dot([(i-10)*5,30,0]).set_opacity(0.5)
            if i==10:
                line2=Line(dot3,dot4).set_color(WHITE).set_opacity(0.5)
                
            else:
                line2=Line(dot3,dot4).set_color(WHITE).set_opacity(0.5)
            self.add(dot3,dot4,line2)
        #设置三个点
        dot1 = Dot(radius=1, color=RED)  
        dot1.move_to([-47.5,27.5,0]) 
        dot2 = Dot(radius=1, color=YELLOW)  
        dot2.move_to([-42.5,27.5,0])  
        dot3 = Dot(radius=1, color=GREEN)  
        dot3.move_to([-37.5,27.5,0])
        #镜头跟进效果 
        self.camera.frame.save_state()
        #题目出现
        
        text = Tex(r"$\int _{0}^{\pi }\dfrac{x}{2+\sin x}dx$"
                   ,tex_template=TexTemplateLibrary.ctex).scale(5.0).move_to([0,20,0])
        text3 = Tex(r"\text{芳900例1:}",color=YELLOW
                   ,tex_template=TexTemplateLibrary.ctex).scale(5.0).next_to(text,LEFT,buff=1)
        text1 = Tex(
                   r"$f\left( x\right) =\dfrac{1}{2+\sqrt{1-x^{2}}}+\dfrac{1}{1+\cos \dfrac{\pi }{2}x+2\sin \dfrac{\pi }{2}x}\int _{0}^{1}f\left( x\right) dx$"
                   ,tex_template=TexTemplateLibrary.ctex).scale(5.0).move_to([5,19,0])
        text4 = Tex(
                   r"\text{芳900例2:}",color=YELLOW
                   ,tex_template=TexTemplateLibrary.ctex).scale(5.0).move_to([-35,20,0])
        text2 = Tex(r"\text{求}$f\left( x\right)$"
                   ,tex_template=TexTemplateLibrary.ctex).scale(5.0).move_to([-23,12,0])
        self.play(Write(text1),self.camera.frame.animate.scale(0.9),Write(text2),Write(text4))
        
        #镜头拉回
          #分析文本
        #text100=MarkupText("<b><i>分析/解：</i></b>",color=PINK).scale(5.0).move_to([-38,12.5,0])
        self.play(Restore(self.camera.frame))
        self.play(FadeIn(dot1),run_time=0.1)
        self.play(FadeIn(dot2),run_time=0.1)
        self.play(FadeIn(dot3),run_time=0.1)
        #self.play(text.animate().scale(1).shift(LEFT*12),text3.animate().scale(1).shift(LEFT*12)) 
        #第一步
        #框框标记
        rectangle=Rectangle(color=BLUE,fill_opacity=0.0,width=10,height=5
                            ,stroke_color=BLUE,stroke_width=20)
        rectangle.move_to([-22.5,12.5,0])
        rectangle1=Rectangle(color=BLUE,fill_opacity=0.0,width=12,height=8
                            ,stroke_color=BLUE,stroke_width=20)
        rectangle1.move_to([31,20,0])
        self.play(Create(rectangle))
        self.play(
            ReplacementTransform(rectangle,rectangle1)
        )
        self.wait(0.5)
        text5 = Tex(
                   r"A",color=RED
                   ,tex_template=TexTemplateLibrary.ctex).scale(7.0).move_to([30,10,0])
        self.play(Create(text5))

        #箭头
        arrow = Arrow(start=[0,12.5,0],end=[0,5,0],color=RED
                       , stroke_width=20, tip_length=1)
        text6 = Tex(
                   r"\text{两边积分}",color=GREEN
                   ,tex_template=TexTemplateLibrary.ctex).scale(7.0).move_to([10,9,0])
        self.play(GrowArrow(arrow),Write(text6))
        text7 = Tex(
                   r"$A=\int ^{1}_{0}\dfrac{1}{2+\sqrt{1-x^{2}}}dx+A\int ^{1}_{0}\dfrac{1}{1+\cos \dfrac{\pi }{2}x+\sin \dfrac{\pi }{2}x}dx$"
                   ,tex_template=TexTemplateLibrary.ctex).scale(7.0).move_to([0,0,0])
        self.play(Write(text7))
         #箭头引出
        arrow1 = Arrow(start=[-40,-10,0],end=[-30,-5,0], color=RED
                       , stroke_width=20, tip_length=1)
        self.play(Create(arrow1))
        #文本
        long_text=("特征识别:\n"
                     "三角换元")
        text8 = Text(long_text,color=YELLOW,
                   font_size=200).move_to([-40,-15,0])
        self.play(Create(text8))



        arrow2 = Arrow(start=[-20,-4,0],end=[-20,-14,0],color=RED
                       , stroke_width=20, tip_length=1)
        text9 = Tex(
                   r"$x=\sin t$",color=GREEN
                   ,tex_template=TexTemplateLibrary.ctex).scale(7.0).move_to([-10,-6,0])
        self.play(GrowArrow(arrow2),Write(text9))
        text10 = Tex(
                   r"$\int _{0}^{\frac{\pi }{2}}\dfrac{\cos t}{2+\cos t}dt$"
                   ,tex_template=TexTemplateLibrary.ctex).scale(7.0).move_to([-20,-20,0])
        self.play(Write(text10))
        text11 = Tex(
                   r"$\int _{0}^{\frac{\pi }{2}}\left( 1-\dfrac{2}{2+\cos t}\right) dt$"
                   ,tex_template=TexTemplateLibrary.ctex).scale(7.0).move_to([-20,-20,0])
        self.play(
            ReplacementTransform(text10,text11)
        )
        self.wait(0.5)




        arrow2 = Arrow(start=[25,-4,0],end=[25,-14,0],color=RED
                       , stroke_width=20, tip_length=1)
        text9 = Tex(
                   r"$t=\dfrac{\pi }{2}x$",color=GREEN
                   ,tex_template=TexTemplateLibrary.ctex).scale(7.0).move_to([35,-12,0])
        self.play(GrowArrow(arrow2),Write(text9))
        text10 = Tex(
                   r"$\dfrac{2}{\pi }\int _{0}^{\frac{\pi }{2}}\dfrac{1}{1+\cos t+2\sin t}dt$"
                   ,tex_template=TexTemplateLibrary.ctex).scale(7.0).move_to([25,-20,0])
        self.play(Write(text10))
        

        self.wait()